On oscillatory nonlinear fourth-order difference equations with delays

Arun K. Tripathy

Mathematica Bohemica (2018)

  • Volume: 143, Issue: 1, page 25-40
  • ISSN: 0862-7959

Abstract

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In this work, oscillatory behaviour of solutions of a class of fourth-order neutral functional difference equations of the form Δ 2 ( r ( n ) Δ 2 ( y ( n ) + p ( n ) y ( n - m ) ) ) + q ( n ) G ( y ( n - k ) ) = 0 is studied under the assumption ∑ n = 0 ∞ n r ( n ) < ∞ . New oscillation criteria have been established which generalize some of the existing results in the literature.

How to cite

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Tripathy, Arun K.. "On oscillatory nonlinear fourth-order difference equations with delays." Mathematica Bohemica 143.1 (2018): 25-40. <http://eudml.org/doc/294668>.

@article{Tripathy2018,
abstract = {In this work, oscillatory behaviour of solutions of a class of fourth-order neutral functional difference equations of the form \begin\{equation*\} \Delta ^\{2\}(r(n)\Delta ^\{2\}(y(n)+p(n)y(n-m)))+ q(n)G(y(n-k))=0 \end\{equation*\} is studied under the assumption \begin\{equation*\} \sum \_\{n=0\}^\{\infty \}\frac\{n\}\{r(n)\}< \infty . \end\{equation*\} New oscillation criteria have been established which generalize some of the existing results in the literature.},
author = {Tripathy, Arun K.},
journal = {Mathematica Bohemica},
keywords = {oscillation; nonlinear; delay; neutral functional difference equation},
language = {eng},
number = {1},
pages = {25-40},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On oscillatory nonlinear fourth-order difference equations with delays},
url = {http://eudml.org/doc/294668},
volume = {143},
year = {2018},
}

TY - JOUR
AU - Tripathy, Arun K.
TI - On oscillatory nonlinear fourth-order difference equations with delays
JO - Mathematica Bohemica
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 143
IS - 1
SP - 25
EP - 40
AB - In this work, oscillatory behaviour of solutions of a class of fourth-order neutral functional difference equations of the form \begin{equation*} \Delta ^{2}(r(n)\Delta ^{2}(y(n)+p(n)y(n-m)))+ q(n)G(y(n-k))=0 \end{equation*} is studied under the assumption \begin{equation*} \sum _{n=0}^{\infty }\frac{n}{r(n)}< \infty . \end{equation*} New oscillation criteria have been established which generalize some of the existing results in the literature.
LA - eng
KW - oscillation; nonlinear; delay; neutral functional difference equation
UR - http://eudml.org/doc/294668
ER -

References

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  1. Agarwal, R. P., Difference Equations and Inequalities: Theory, Methods, and Applications, Pure and Applied Mathematics 228. Marcel Dekker, New York (2000). (2000) Zbl0952.39001MR1740241
  2. Agarwal, R. P., Grace, S. R., Wong, P. J. Y., Oscillation of fourth order nonlinear difference equations, Int. J. Difference Equ. 2 (2007), 123-137. (2007) MR2493593
  3. Bohner, M., Peterson, A., 10.1007/978-1-4612-0201-1, Birkhäuser, Basel (2001). (2001) Zbl0978.39001MR1843232DOI10.1007/978-1-4612-0201-1
  4. Bohner, M., Peterson, A., 10.1007/978-0-8176-8230-9, Birkhäuser, Boston (2003). (2003) Zbl1025.34001MR1962542DOI10.1007/978-0-8176-8230-9
  5. Graef, J. R., Miciano, A., Spikes, P., Sundaram, P., Thandapani, E., 10.1017/S0334270000000552, J. Aust. Math. Soc., Ser. B 38 (1996), 163-171. (1996) Zbl0890.39018MR1414357DOI10.1017/S0334270000000552
  6. Graef, J. R., Thandapani, E., Oscillatory and asymptotic behaviour of fourth order nonlinear delay difference equations, Fasc. Math. 31 (2001), 23-36. (2001) Zbl1009.39007MR1860547
  7. Gyori, I., Ladas, G., Oscillation Theory for Delay Differential Equations with Applications, Oxford Mathematical Monographs. Clarendon Press, Oxford (1991). (1991) Zbl0780.34048MR1168471
  8. Migda, M., Asymptotic properties of nonoscillatory solutions of higher order neutral difference equations, Opusc. Math. 26 (2006), 507-514. (2006) Zbl1131.39008MR2280277
  9. Migda, M., Migda, J., 10.1080/10236190903032708, J. Difference Equ. Appl. 15 (2009), 1077-1084. (2009) Zbl1194.39009MR2569136DOI10.1080/10236190903032708
  10. Parhi, N., Tripathy, A. K., 10.1016/S0022-247X(03)00298-1, J. Math. Anal. Appl. 284 (2003), 756-774. (2003) Zbl1037.39002MR1998666DOI10.1016/S0022-247X(03)00298-1
  11. Thandapani, E., Arockiasamy, I. M., Oscillatory and asymptotic behaviour of fourth order nonlinear neutral delay difference equations, Indian J. Pure Appl. Math. 32 (2001), 109-123. (2001) Zbl1004.39005MR1819234
  12. Thandapani, E., Sundaram, P., Graef, J. R., Miciano, A., Spikes, P., Classification of non-oscillatory solutions of higher order neutral type difference equations, Arch. Math. (Brno) 31 (1995), 263-277. (1995) Zbl0855.39014MR1390585
  13. Tripathy, A. K., Oscillation of fourth-order nonlinear neutral difference equations II, Math. Slovaca 58 (2008), 581-604. (2008) Zbl1199.39018MR2434679
  14. Tripathy, A. K., New oscillation criteria for fourth order nonlinear neutral difference equations, Adv. Dyn. Syst. Appl 8 (2013), 387-399. (2013) MR3162156

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